This research was supported in part by Institute for Mathematics and its Applications
Finite element method, Galerkin methods, Multigrid methods (Numerical analysis)
A variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion problem, for which an error estimate is proved. A multigrid algorithm for this method is presented, and numerical experiments indicating its robustness with respect to diffusion coefficient are reported.
Gopalakrishnan, Jay and Kanschat, Guido, "A Multilevel Discontinuous Galerkin Method" (2003). Mathematics and Statistics Faculty Publications and Presentations. 73.